Enter a whole number to list every one of its factors, plus the factor count, factor sum, and its perfect/abundant/deficient classification.

How to Use the Factor Calculator

Type the number into the field and the results populate underneath immediately — no separate button to press, no mode to pick first.

This isn't the same job as prime factorization. The Prime Factorization Calculator elsewhere on this site breaks a number down into its prime building blocks only — 36 becomes 2² × 3² and stops there. This tool goes wider: it lists literally every number that divides into your input evenly, primes and composites both.

Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36

Nine factors, not the two primes that show up in 36's prime factorization. The method is blunt by design — check every integer from 1 up to the number itself, keep whichever ones divide in without a remainder. Very large inputs are capped at 1,000,000 to keep the browser responsive.

What Makes a Number Perfect

Add up a number's factors excluding itself, then compare that sum back to the number. Three things can happen: the sum falls short (deficient), matches exactly (perfect), or overshoots (abundant).

6 = 1 + 2 + 3 (perfect)
12 = 1 + 2 + 3 + 4 + 6 = 16 (abundant)
9 = 1 + 3 = 4 (deficient)

Perfect numbers are rare enough that people have been tracking them since antiquity — 6 and 28 are the two smallest, and both were known to the ancient Greeks. Euclid proved a rule for generating even perfect numbers over two thousand years ago, and to this day nobody has found an odd one or proven none exists. That's still an open problem in number theory.

Most numbers you type in will land on deficient. Abundance and perfection both get rarer climbing upward, though abundant numbers turn up more often than perfect ones — 12, 18, 20, and 24 are all abundant.